Supervision of Petri Nets

1. The Petri Net Model.- 1 Discrete event systems.- 2 Notation.- 3 Order theoretical preliminaries.- 4 Petri net definition.- 5 Petri nets as discrete event system models.- 6 Reachable sets.- 7 Graphical representation.- 8 Reachability via subsets of transitions.- 9 Other concurrency assumptions.- 10 A general Petri net definition.- 11 Notes and references.- 2. Supervisory Control.- 1 Control goal and architecture.- 2 Formal definition.- 3 Reachable sets under supervision.- 4 Maximally permissive control laws.- 5 Specific control sets.- 6 Linear inequalities as a legal set.- 7 Control design under the no concurrency assumption.- 8 Notes and references.- 3. Uncontrollable Events And Transitions.- 1 Introduction.- 2 Supervisory control laws.- 3 Specific concurrency and control assumptions.- 4 Maximally permissive control laws.- 5 Control design.- 6 The supremal controllable subset.- 7 Notes and references.- 4. Reduction Theorems.- 1 Intuition for A*.- 2 Invariance properties of the legal set.- 3 Sets of places and transitions.- 4 Reduction result for A*.- 5 Reduction of the control design.- 6 Structural and invariance properties of the legal set.- 7 Notes and references.- 5. Acyclic Petri Nets.- 1 Partitioning of the sets of places and transitions.- 2 Structure of the incidence matrices.- 3 Reachability in acyclic Petri nets.- 4 A reachability algorithm.- 5 Acyclic Petri nets free of choice places.- 6 Construction of the supremal controllable subset.- 7 Notes and references.- 6. Decomposition Of The Control Design.- 1 Introduction.- 2 Unions of legal sets.- 3 A uxiliary results.- 4 Proof of Theorem 6.1.- 5 Discussion.- 6 Control design.- 7 Notes and references.- 7. Continuous Versus Discrete Events.- 1 Continuous Petri nets.- 2 A subset of the supremal controllable subset.- 3 Construction of the supremal controllable subset.- 4 No synchronising transitions in NAuc.- 5 No choice places in NAuc.- 6 A third class.- 7 Structure of A*.- 8 Notes and references.- 8. Structural Linear Algebraic Control Design.- 1 Unobservable events.- 2 Overview of the approach.- 3 Intersection of a linear halfspace with the first orthant.- 4 Candidate sets A??.- 5 Maximal sets A??.- 6 Reduction of controllers with disjunctions.- 7 A subset of the supremal controllable subset.- 8 Notes and references.- References.